Lectures for a semester-long flipped course on quantum mechanics

What you'll learn

Introduction to fundamental principles and the need for quantum mechanics
Domain of quantum mechanics and its applicability to microscopic systems
Key concepts such as wave-particle duality, quantization, and superposition
Complex numbers and their role in quantum mechanics
Probability theory, probability distributions, and variance in quantum mechanics
Concept and physical meaning of the wavefunction
Normalization of the wavefunction and its importance
Extracting position, velocity, and momentum from the wavefunction
Heisenberg's uncertainty principle and its implications
Derivation and interpretation of Schrodinger's equation
Separation of variables and stationary states in quantum systems
Superposition of stationary states and their physical consequences
Potential functions and their impact on quantum behavior
Infinite square well (particle in a box) and its quantized energy states
Orthogonality and completeness of quantum states
Fourier series applications in quantum mechanics
Quantum harmonic oscillator using ladder operators and power series solutions
Free particles and their corresponding wavefunctions
Example computations and simulations for quantum systems

Requirements

Basic Mathematics – Algebra, trigonometry, and exponentials/logarithms
Complex Numbers – Understanding ? = − 1 i= −1 ​ and simple operations
Probability – Basic ideas of probability and distributions
Basic Physics – Newton's laws, energy, and momentum

Description

Course

Overview

This course offers a clear and approachable introduction to quantum mechanics, designed to guide students, professionals, and enthusiasts through the essential concepts, mathematical tools, and real-world applications of this exciting field. Whether you're a student looking to understand the foundations of quantum physics or a curious mind eager to dive into one of science's most fascinating areas, this course will provide you with a solid grounding in quantum mechanics.What You Will LearnBy the end of this course, you will have a deep understanding of the following core topics:Fundamental Concepts:Understand the key principles of quantum mechanics, including wave-particle duality, quantization, and the superposition principle.The Wavefunction & Its Properties:Learn how the wavefunction represents quantum systems and how to calculate probabilities, positions, momentum, and more.Schrödinger Equation:Dive into the Schrödinger equation and its role in describing quantum systems, with an emphasis on separation of variables and solving for stationary states.Uncertainty Principle:Grasp the implications of Heisenberg's uncertainty principle and how it defines the limits of measurement in quantum mechanics.Advanced Quantum Systems:Explore the infinite square well (particle in a box), quantum harmonic oscillators, free particles, and scattering phenomena.Mathematical Tools:Learn the mathematical foundations, including complex numbers, linear algebra (eigenvalues, eigenvectors), and the use of Fourier series in quantum mechanics.Applications:Apply your knowledge to real-world systems, such as the hydrogen atom and its wavefunctions, angular momentum in quantum mechanics, and spin 1/2 particles.Quantum Mechanics in Practice:Develop practical skills in quantum simulations and calculations, gaining insight into how quantum mechanics influences modern technology and research.

Who this course is for

Physics and Engineering Students: Those studying quantum mechanics as part of their curriculumSTEM Enthusiasts: Anyone curious about the fundamental principles of quantum physicsMathematics Students: Individuals interested in the mathematical foundations of quantum mechanicsSelf-Learners: Anyone with a basic background in math and physics who wants to explore quantum mechanicsResearchers and Professionals: Scientists or engineers looking for a refresher on quantum principles and their applicationsNo previous experience with quantum mechanics is required—just a basic understanding of math and physics will help you succeed!Why Take This Course?Quantum mechanics is the foundation of modern physics, providing the framework for understanding the behavior of particles at the microscopic scale. This course will empower you with the knowledge to understand the quantum world, a realm where classical physics breaks down and strange phenomena like wave-particle duality, superposition, and entanglement reign. By learning quantum mechanics, you'll gain insight into a variety of real-world applications, such as semiconductors, quantum computing, and molecular chemistry.Whether you're preparing for advanced studies, looking to apply quantum mechanics in your research, or simply curious about the quantum nature of the universe, this course will give you the tools to begin that journey with confidence.Enroll NowDive into the quantum realm and gain a deeper understanding of the universe. Let's explore the world of quantum mechanics together!

Who this course is for

Physics and Engineering Students – Those studying quantum mechanics as part of their curriculum
STEM Enthusiasts – Anyone curious about the fundamental principles of quantum physics
Mathematics Students – Those interested in the mathematical foundations of quantum theory
Self-Learners – Individuals with a basic background in math and physics who want to explore quantum mechanics
Researchers and Professionals – Scientists or engineers looking for a refresher on quantum principles
Homepage:

https://www.udemy.com/course/foundations-of-quantum-mechanics/